Question

Calculate the ratio of the angular momentum of the earth about its axis due to its spinning motion to that about the sun due to its orbital motion. Radius of the earth = 6400 km and radius of the orbit of the earth about the sun = 1.5 $\times {10}^8$ km.

Answer 1

Angular momentum of the earth about its axis

=$\frac{2}{5}m{r}^2\left(\frac{2\pi }{86400}\right)$

$(\text{because,}I=\frac{2}{5}m{r}^2)$

Angular momencum of the earth about sun's axis

$=m{R}^2\times (\frac{2\pi }{86400}\times 365)$

$(\text{because,}I=m{R}^2)$

Therefore, Ratio of the angular momentum

$=\frac{\frac{2}{5}m{r}^2\times \left(\frac{2\pi }{86400}\right)}{m{R}^2\times \frac{2\pi }{(86400\times 365)}}$

$=\frac{(2r^2\times 365)}{5R^2}=\left(\frac{2.990\times {10}^{10}}{1.125\times \times {10}^{17}}\right)$

$=2.65\times {10}^{-7}$